2a. Answer: 100
Step-by-step explanation:
[tex]Area_{\ shaded\ region}=Area_{\ parallelogram}-Area_{\ triangle}\\\\Area_{\ parallelogram}=base \times height\\\\.\qquad \qquad \qquad \qquad =14\times 10\\\\.\qquad \qquad \qquad \qquad =140\\\\Area_{\ triangle}=\dfrac{base\times height}{2}\\\\\\.\qquad \qquad \quad =\dfrac{8\times 10}{2}\\\\\\.\qquad \qquad \quad =40\\\\Area_{\ shaded\ region}=140-40\\\\.\qquad \qquad \qquad \qquad =100[/tex]
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2b. Answer: 114
Step-by-step explanation:
[tex]Area_{\ shaded\ region}=Area_{\ trapezoid}-Area_{\ kite}\\\\Area_{\ trapezoid}=\dfrac{base_1+base_2}{2}\times height\\\\\\.\qquad \qquad \qquad =\dfrac{11+18}{2}\times (5+7)\\\\\\.\qquad \qquad \qquad =\dfrac{29\times 12}{2}\\\\\\.\qquad \qquad \qquad =174\\\\\\Area_{\ kite}=\dfrac{diagonal_1\times diagonal_2}{2}\\\\\\.\qquad \qquad=\dfrac{(5+5)(5+7)}{2}\\\\\\.\qquad \qquad=\dfrac{10\times 12}{2}\\\\\\.\qquad \qquad=60[/tex]
[tex]Area_{\ shaded\ region}=174-60\\\\.\qquad \qquad \qquad \qquad =114[/tex]
